Before studying the decays, we need to briefly introduce the \(4S\) -\(3D\)  mixing scheme. If assigning the \(\Upsilon (10753)\)  as the pure \(\Upsilon (3D)\)  state, the predicted mass of pure \(\Upsilon (3D)\)  state ranges from 10653 MeV to 10717 MeV [1]}, [2]}, [3]}, [4]}, [5]}. Thus, there exists difference between the theoretical result and current measurement of the \(\Upsilon (10753)\) . Furthermore, the dielectron width of the \(\Upsilon (3D)\)  was estimated to be just a few eV [3]}, [5]}, [1]}, [2]}, which is lower than the corresponding dielectron widths of the \(\Upsilon (4S)\)  and \(\Upsilon (5S)\)  states. Thus, it is difficult to find pure \(\Upsilon (3D)\)  state via the electron-positron annihilation process. However, the \(\Upsilon (10753)\)  signal was observed in the \(e^{+}e^{-}\rightarrow \Upsilon (nS)\pi ^{+}\pi ^{-}\)  processes by Belle [10]}, which is puzzling for us.
As proposed in Refs. [11]}, [12]}, the \(4S\) -\(3D\)  mixing scheme for the \(\Upsilon (10753)\)  was introduced
\(\left(\begin{array}{c}\Upsilon _{4S-3D}\\\Upsilon ^{\prime }_{4S-3D}\end{array}\right)=\left(\begin{array}{cc}\cos {\theta } & -\sin {\theta }\\\sin {\theta } & \cos {\theta }\end{array}\right)\left(\begin{array}{c}\Upsilon ({4S})\\\Upsilon ({3D})\end{array}\right),\) 
